View source for Scalar

'''Scalars''' are simple [[number]]s. They are used for [[measurement|measuring]] things. Many things can be measured, and the measure can be explained by only giving the number.

Suppose we are measuring a [[rod]]. We could give the measured [[length]] as 2 [[metre]]s or 3 cm—depending on the length of the rod under observation. Here, only the figure 2 or 3 along with the [[unit]] of measure is enough to transmit information about the rod.

Other examples of scalars are: 
*Unit of [[mass]] ([[Kilogram]]s)
*Unit of measuring [[luminosity]] ([[Candela]])
*Unit of length (Metres)

In other words, mass is measured by scalars, just like [[distance]]s are measured by scalars.

In [[mathematics]], scalars are distinguished from more complex mathematical objects such as [[Vector|vectors]] and [[Matrix (mathematics)|matrices]] in that they consist of only one number. A scalar <math>k</math> can also be multiplied to a vector <math>\mathbf{v}</math> or a matrix <math>A</math>, resulting in the vector <math>k\mathbf{v}</math> and the matrix <math>kA</math>, respectively.<ref>{{Cite web|date=2020-03-25|title=Comprehensive List of Algebra Symbols|url=https://mathvault.ca/hub/higher-math/math-symbols/algebra-symbols/|access-date=2020-09-06|website=Math Vault|language=en-US}}</ref> For vectors, scalar multiplication produces a new vector of different length in the same or opposite direction of the original vector.<ref>{{Cite web|last=Weisstein|first=Eric W.|title=Scalar Multiplication|url=https://mathworld.wolfram.com/ScalarMultiplication.html|access-date=2020-09-06|website=mathworld.wolfram.com|language=en}}</ref>

== Related pages ==

* [[Dot product]], a scalar quantity
* [[Scalar (physics)]]

== References ==
<references />
{{Math-stub}}
[[Category:Measurement]]
[[Category:Basic physics ideas]]